标题： 独立规范的真空球对称时空摄动的度规重构 显示英文标题

标题： Gauge-Independent Metric Reconstruction of Perturbations of Vacuum Spherically-Symmetric Spacetimes

摘要： 真空球对称时空的微扰理论（包括宇宙常数）在理解黑洞、相对论性致密星甚至非齐次宇宙学模型方面做出了巨大贡献。 可以通过满足$1+1$波动方程的（规范不变的）主函数将微扰方程组分离。 在这项工作中，基于之前关于主函数和方程空间结构的研究，我们研究了用主函数重构度规微扰的方法。 为此，我们考虑了一般情况，即微扰由任意的能量-动量张量驱动。 然后，在完全一般的微扰规范下执行度规重构。 在此过程中，我们探讨了达布变换和达布协变性的作用，它们在没有物质源的情况下负责奇偶宇称之间的等谱性，以及基于所有可能的主方程描述的物理等价性。 我们还表明，度规重构可以使用任何可能的主函数来完成，并且这些表达式具有显式的协变形式。 显示英文摘要

摘要： Perturbation theory of vacuum spherically-symmetric spacetimes (including the cosmological constant) has greatly contributed to the understanding of black holes, relativistic compact stars and even inhomogeneous cosmological models. The perturbative equations can be decoupled in terms of (gauge-invariant) master functions satisfying $1+1$ wave equations. In this work, building on previous work on the structure of the space of master functions and equations, we study the reconstruction of the metric perturbations in terms of the master functions. To that end, we consider the general situation in which the perturbations are driven by an arbitrary energy-momentum tensor. Then, we perform the metric reconstruction in a completely general perturbative gauge. In doing so, we investigate the role of Darboux transformations and Darboux covariance, responsible for the isospectrality between odd and even parity in the absence of matter sources and also of the physical equivalence between the descriptions based on all the possible master equations. We also show that the metric reconstruction can be carried out in terms of any of the possible master functions and that the expressions admit an explicitly covariant form.